Shoot the Dragon

Normally, when a villain kills off a minion, it is for You Have Failed Me... or You Have Outlived Your Usefulness reasons, but not always. Sometimes, the minion in question is a complete psycho, and their superior will off them themselves (or congratulate the heroes if they do). The reasons for doing this vary, but are generally some combination of fear of the psycho becoming The Starscream, fear that the psycho is so unstable that they will ruin the boss' schemes, and Even Evil Has Standards.

As a Death Trope, Spoilers ahead may be unmarked. Beware.

Examples of Shoot the Dragon include:

Anime and Manga

In Dragonball Z, Freeza blew up an entire planet because he was afraid the Saiyans that served as his low class soldiers could grow to overpower him.
In Baccano!, Mafia Don Bartolo Runorata sets Gustavo Bagetta up against the Gandor Family in order to get rid of him after Gustavo becomes more trouble than he's worth. In the anime, Don Bartolo ends up blowing Gustavo away personally as a gesture of good faith to Eve Genoard; in the Light Novels, Luck Gandor does the honors, but not before pointing out to Gustavo that Don Bartolo is aware of his shenanigans and will be glad to be rid of him.
Kind of twisted example in Black Lagoon. A Magnificent Bastard Nazi Aristocrat tires of the incompetence of his Neo-Nazi followers, so he sends them on an assignment which leads to their coming in conflict with the protagonists. After the Neo-Nazis are all killed by the protagonists (well, mainly Revy and Dutch), the leader congratulates Dutch and tells him You Are a Credit to Your Race. He wasn't necessarily planning on their deaths, but more as a test, which if they didn't succeed, they weren't worth keeping alive.

Literature

In The Three Musketeers, Richelieu is happy for this reason when the heroes kill Milady and gives D'Artagnan a promotion/job as a reward. While the Cardinal was willing to use her services, he's Affably Evil, whereas she was a psycho vamp and thus he was happy to be rid of her.
In the Discworld/Hogfather, the head of the Assassins' Guild, Lord Downey is shown considering the possibility of offing the Psycho for Hire assassin student, Jonathan Teatime. It's partly Even Evil Has Standards, but also practically speaking, Downey knows that Teatime is stealthy enough to sneak into his study undetected and crazy enough to kill him if the whim should take him.
In the Vorkosigan Saga- the Lawful Evil Emperor Ezar is believed by those in the know to have deliberately launched an invasion of Escobar which was doomed to fail, so that he could kill his son Prince Serg and discredit the violent nationalists at his court. The sacrifice of numerous innocents during that invasion made it possible for the throne to pass to Ezar's grandson, Gregor, who is a noble and benevolent Guy Wearing the Kingly Mask
In Joseph Conrad's novel Under Western Eyes, one character (based on a real person) is a Psycho for Hire who has infiltrated the Bomb-Throwing Anarchists. He's a Tsarist agent whose employers basically give him carte blanche to kill his own allies and basically conduct false flag operations to make anarchists look bad. After he severely injures the protagonist, a Hero Antagonist Secret Police officer lets the anarchists know of the traitor in their midst, and there's a description of the psycho being cornered by anarchists on a train with an implied Gory Discretion Shot.

Video Games

Sigma in Mega Man Xtreme 2 thanks X and Zero for taking care of Berkana, saying she went too far and was too greedy with the power she was taking.

Web Original

The Evil Overlord List permits this, but only on the understanding that the Evil Overlord is then forbidden to ask why he is surrounded by idiots.